Fast neutron spectroscopy with tensioned metastable fluid detectors

ABSTRACT

Systems and methods for neutron detection using tensioned metastable fluid detectors, using a single atom spectroscopy approach.

The present application claims the benefit of the filing date of U.S.provisional application Ser. No. 62/398,572, filed 23 Sep. 2016, thecontents of which are incorporated herein by reference.

GOVERNMENT SUPPORT CLAUSE

This invention was made with government support under DGE-0833366 andDGE-1333468 awarded by the National Science Foundation. The governmenthas certain rights in the invention.

TECHNICAL FIELD

The present application relates to systems and methods for neutrondetection, and in particular to methods for neutron detection associatedwith tensioned metastable fluid detectors.

BACKGROUND

This section introduces aspects that may help facilitate a betterunderstanding of the disclosure. Accordingly, these statements are to beread in this light and are not to be understood as admissions about whatis or is not prior art.

The ability to perform neutron spectroscopy offers significant benefitsespecially when using tensioned metastable fluid detectors (TMFDs) whichoffer unique advantages relative to state of art systems.

It is well-known that neutron detection with spectroscopy is ofsignificant importance in a wide range of fields ranging fromfundamental physics to nuclear power to combatting nuclear terrorism.Tension Metastable Fluid Detector (TMFD) technology offers a uniquealternative to conventional neutron detectors for a wide array ofapplications. Highlights of TMFD capabilities include but are notlimited to: high intrinsic efficiency for both fast and thermalneutrons, on-off times on the order of microseconds to allow phaselocking with pulsed interrogation sources for active interrogation,gamma blindness to vastly decrease nuisance (interfering) background andallow active photon interrogation, single system directionalitycapabilities, the ability to extend to alpha and fission productdetection, promising capability to perform neuron multiplicityassessments, the ability to change sensitivity on demand, andpotentially with significant reduced cost and complexity of operationwhen compared to the state of the art.

Despite strong performance as a detector, usefulness of TMFDs in dosemeasurements or spectrometry requires knowledge of the response functionto relate the tension state of the detector with the amount of energydeposited (by incoming radiation over nanometer scales) to thepropensity to generate a Cavitation Detection Event (CDE). Thisconstituted a key piece of information which, until now has remainedintractable to assess with any reasonable level of accuracy. Themainstay elegantly simple so-called Thermal Spike Theory (TST) whichrobustly predicts CDEs for thermally superheated metastable fluids forbubble chambers fails, when applied to tensioned (room temperature)metastable fluids to describe the manifestation of CDEs. As vividly seenfrom Table 1, TST predicts energy barriers to nucleation of cavities intensioned metastable state fluids that are more than an order ofmagnitude smaller than the barrier encountered experimentally.

TABLE 1 Predicted (thermal-spike-theory) and actual TMFD experimentalenergy barrier for detecting ²¹⁰Po alpha recoils in acetone (at 20° C.and P_(neg) = −8.3 bar). Energy Barrier Components Energy (keV) Surface(Tension) energy 5.7 Expansion work (pdV) 3.9 Evaporation energy 2Kinetic energy given to liquid 0 Viscous energy loss 2.1 Total predictedenergy barrier 13.7 Actual ion recoil energy [3] 101

As a result, applying TST to predict outcomes from TMFD experimentsresults in far more predicted CDEs than actually observedexperimentally. Without the ability to model detector response for CDEswith reasonable accuracy for neutrons of different energies, ittherefore, has remained unrealized to develop response matrices and todistinguish a large flux of particles with a small interactioncross-section from a small flux of particles with a large cross-section.While response curves for any arbitrary neutron source in a givensource-detector geometry can be obtained experimentally and used toestimate the intrinsic TMFD detection efficiency, the spectralidentification of an arbitrary neutron source in an arbitrary geometryrequires rigorous knowledge of the TMFD's response function.

There is, therefore an unmet need for a novel approach to identify aresponse function to relate the tension state of the detector with theamount of energy deposited (by incoming radiation over nanometer scales)to the propensity to generate a CDE.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic representation of a Centrifugally TensionedMetastable Fluid Detector (CTMFD) sensor system according to the presentdisclosure.

FIG. 2 shows relative energy deposition by carbon and hydrogen in 1825Angstrom critical bubble diameter in Heptane as modeled in SRIM.

FIG. 3 shows a TMFD detection fluid enthalpy of vaporization versustension pressure thresholds for detecting fast neutrons from a Pu—Beisotope neutron source.

FIG. 4 shows a CTMFD system geometry as modeled for MCNPX-POLIMI codecalculations.

FIG. 5 shows frequency of induced recoils in Heptane versus recoilenergy of C atoms when subject to neutrons emitted from a Pu—Be isotopeneutron source positioned about 35 cm from the CTMFD bulb.

FIG. 6 shows MCNP predicted recoil spectrum in comparison withexperimental neutron detection rates at various |P_(neg)| statescorresponding to recoil energy for nucleation.

FIG. 7 shows variations of carbon recoil induced energy threshold for aCDE to occur versus the corresponding centerline |P_(neg)|.

FIG. 8 shows a relative count graph of neutron energy for a responsematrix of the CTMFD system, relating detection rates for neutrons ofvarious energies.

FIG. 9 shows relative response versus neutron energy for PuBe neutronsource spectrum and unfolded approximation using volume averaged modelof CTMFD detection volume.

FIG. 10 shows the sensitivity regions in the detector bulb volume as theCTMFD rotates more rapidly.

FIG. 11 shows carbon recoil energy versus |P_(neg)| for volume averagedand LP integer program models.

FIG. 12 shows relative count of neutron energy for a response matrixcorresponding to the power law lift of FIG. 11.

FIG. 13 shows relative response of neutron energy for Cf-252 neutronsource spectrum and corresponding unfolded approximation.

FIG. 14 shows carbon recoil energy versus carbon recoil range for acalculated carbon recoil range curve in heptane.

FIG. 15 shows predicted energy barrier in heptane versus |P_(neg)|,comparing predicted required energy thresholds for CDEs from neutroninduced C recoils versus |P_(neg)| for various techniques withpredictions from Thermal Spike Theory.

FIG. 16 is a schematic diagram for a system comprising detectors forsolving a vector matrix equation relating to relative detection time fora range of P_(neg) states.

FIG. 17 is a flowchart outlining operations embodied in the presentdisclosure.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of thepresent disclosure, reference will now be made to the embodimentsillustrated in the drawings, and specific language will be used todescribe the same. It will nevertheless be understood that no limitationof the scope of this disclosure is thereby intended.

A novel approach to identify a response function to relate the tensionstate of the detector with the amount of energy deposited (by incomingradiation over nanometer scales) to the propensity to generate aCavitation Detection Event (CDE) is disclosed. To enable the generationof this function for tensioned metastable fluid detectors (TMFDs),Single Atom Spectroscopy (SAS) was developed and constitutes oneembodiment of the subject matter of this disclosure.

The inability of prevailing theoretical models (developed successfullyfor a classical bubble chamber) to adequately predict detectionthresholds for tensioned metastable fluid conditions is presentedherein. To that end, techniques are presented to overcome these inherentshortcomings, leading thereafter, to allow successful neutronspectroscopy using TMFDs—via a newly developed Single Atom Spectroscopy(SAS) approach. SAS also allows for a unique means for rapidlydetermining neutron energy thresholds with TMFDs. This is accomplishedby simplifying the problem of determining Cavitation Detection Events(CDEs) arising from neutron interactions with one in which severalrecoiling atom species contribute to CDEs, to one in which only onedominant recoil atom need be considered. One exemplary fluid is Heptane(C₇H₁₆) for which only recoiling C atoms contribute to CDEs. Using theSAS approach, the threshold curve for Heptane is derived using isotopeneutron source data, and then validated against experiments withmono-energetic (2.45/14 MeV) neutrons from D-D and D-T accelerators.Thereafter the threshold curves are utilized to produce the responsematrix for various geometries. The response matrices are in turncombined with experimental data to recover the continuous spectra offission (Cf-252) and (α,n) Pu—Be isotopic neutron sources via anunfolding algorithm. A generalized method is also presented forperforming neutron spectroscopy using any other TMFD fluid that meetsthe SAS approach assumptions.

TMFDs operate in a manner analogous to causing a tear in a stretchedrubber band. The more one stretches the molecules, the easier it becomesto cause a tear with a given stimulus that provides the excess energy tobreak apart the bonds holding the rubber together (e.g., poking with aneedle). In TMFDs the fluid space is stretched such that particles likeneutrons or other radioactive recoiling nuclei can then provide therequired excess energy to cause a cavitation detection event (CDE). Atensioned metastable fluid becomes selectively sensitive to ion recoilsinduced by neutron interactions when the fluid of the TMFD is tensionedsuch that it attains a sub-atmospheric or even sub-zero (below perfectvacuum) pressure fluid state. As an incident neutron enters the fluidand collides with the nucleus of one of the atoms, the recoiling ionizednucleus then deposits energy through soft and hard interactions withsurrounding fluid molecules resulting in a localized thermallysuperheated cavity in the tens of nanometer range. If the amount ofenergy deposited is not sufficient to overcome the energy barrierimposed for cavitation bubble growth, the vapor cavity will condense andcollapse back into the liquid. If, however, the ion manages to depositenough energy to overcome the required threshold, the cavity will reacha critical size and continue to grow thereafter, in the negativepressure field. In order for this to happen, an amount of energyexceeding the energy barrier must be deposited within a criticaldiameter. The critical radius, r_(e), can be expressed (to the firstorder) in terms of the surface tension, σ, the pressure of the vaporinside the cavity, p_(v), and the pressure of the liquid outside thecavity, p_(l) as described in equation (1) below.

$\begin{matrix}{r_{c} = \frac{2\sigma}{p_{v} - p_{l}}} & (1)\end{matrix}$

In fluid molecules with multiple constituent atoms, each atom in thefluid will need to be given a different amount of energy by impingingradiation (focusing on neutrons) in order to overcome the energybarrier. These energies can vary greatly. The variation is due to adifference in linear energy transfer (LET) over the critical cavitydimension which typically is in the tens of nanometer range (see Table 2for a TMFD fluid such as acetone with dissolved boron). Because both thecritical dimension and the LET are functions of complex fluidproperties, it is highly desirable to find candidate fluids that possessonly a single “dominant” atom. In this way, all recoil atoms generatedby nuclear interactions can be deemed to deposit energy in the samemanner and the only difference that needs to be considered is thestarting energy.

TABLE 2 Linear energy transfer of 1 MeV particles of varied masscalculated via SRIM in a sample fluid [5]. Ion at 1 MeV dE/dx (MeV/cm) e(electron) 1 Hydrogen (Z = 1) 183 Boron (Z = 5) 3768 Carbon (Z = 6) 4217Oxygen (Z = 8) 4455

Even if all the recoils of interest deposit their energy similarly, in apractical system the detection of these recoils could be different dueto a difference in the encountered negative pressure of the fluid at thelocation of the strike. By adding an assumption that the negativepressure field is uniform, it may then be said that all recoils bornwith energy less than the energy that corresponds to the Bragg peak willhave a greater propensity to nucleate and result in a CDE, than ionsborn with lesser energy. Given these stipulations, the CDE threshold cannow be determined by simulating ion recoils, sorting all recoilsgenerated in the TMFD sensitive region by energy, and then finding thespecific energy threshold wherein the number of recoils generated at orabove that energy corresponds to the experimentally obtained detectionrate.

Referring to FIG. 1, a schematic representation of a CentrifugallyTensioned Metastable Fluid Detector (CTMFD) sensor system according tothe present disclosure is presented. CTMFDs as configured induce tensionin a specific sensitive volume by spinning rapidly around the centralaxis. Further description of FIG. 1 is provided in U.S. Pat. No.9,194,966 to Taleyarkhan et al., incorporated by reference in itsentirety into the present disclosure. The liquid in the arms is drawnaway from the axis of rotation towards the elbow of the device. Thetensile force in the fluid arm below the elbow is balanced by thecompressive force in the fluid molecules from above the elbow. Thisarchitecture results in a tension pressure variation in the lower armsabout the central bulb generating the maximum tension pressure (P_(neg))state in the fluid volume at the central axis within the bulb at thebottom. The P_(neg)(r) magnitude can be predicted by a straightforwardapplication of the Bernoulli equation for incompressible fluids asevidenced from Eqs. (2) and (3), provided below. As the rotational speedincreases, for a given combination of fluid density and meniscusseparation, the tension pressure within the CTMFDs sensitive cavity islowered—to the point of overcoming the normal ambient 0.1 MPa (1 bar)pressure, and thereafter, to negative pressure states (i.e., to belowvacuum pressures). The induction of sub-zero pressures in the fluid nowenables incoming ionizing particles like neutrons to deposit energy ontoatoms of the fluid molecules. As explained earlier, this results inrecoiling ions which deposit energy which (if sufficient), to then causelocalized cavitation and bubbles to form that grow to visible-audiblestates and can be recorded.

Once a desired P_(neg) state is achieved a clock is initiated fordetecting incoming neutrons that can cause CDEs. These events result ina fast growing bubble which expands within microseconds to form a vaporcolumn in the interior of the CTMFD's sensitive bulb region. Around thecentral bulb are positioned infrared (IR) beam sensors which then detectthe difference in light transmission upon bubble formation, and theradiation induced CDE is thus recorded and timed. The CTMFD is nominallyoperated with use of LABVIEW based virtual instrument (VI) control-dataacquisition software, but can be operated manually as well. With this IRsensing system and the control software used for the experimentspresented in this specification, CDE's occurring about 0.3 s or more(i.e., the wait time; which translates to rate of detection of about 3s⁻¹ and lower) after reaching the desired P_(neg) were possible to usereliably. This time is also referred to as the “wait-time” which is theinverse of the traditional rate of detection. From a practical sense, asthe source neutron intensity increases, and the time it takes for theCTMFD to detect the neutrons upon reaching the P_(neg) state getstowards 0.3 s, the uncertainty involved in the data rises and hence,conducting SAS for high intensity sources with such a system requiredthat the source-to-detector distance be adjusted accordingly or that,the P_(neg) states be tailored such that the wait time is sufficientlyabove 0.3 s.

Within the central bulb of a Centrifugally Tensioned Metastable FluidDetector (CTMFD) shown in FIG. 1, the pressure gradient from thecenterline to the edge of the central bulb is obtained by arearrangement of the classical Bernoulli equation for incompressiblefluids.

As such, at the centerline axis, the negative pressure (P_(neg)) isexpressed as:

p _(neg)(r=0)=2*π²*ρ_(l) *R ² *f ² −P _(amb)  (2)

The P_(neg), (r), at a location away from the centerline is:

$\begin{matrix}{{p_{neg}(r)} = {\frac{\left( {{p_{neg}(0)} + P_{amb}} \right)\left( {R - r} \right)^{2}}{R^{2}} - P_{amb}}} & (3)\end{matrix}$

The various terms in Eqs. (2) and (3) follow conventional notation inthat P_(neg) (r) is the negative pressure at a given radius (r), ρ_(l)is the density of the liquid, f is the rotational frequency, R is thedistance of the meniscus of the liquid above the elbow from thecenterline, r is the radius at the location being investigated (r=0 atthe centerline), P_(amb) is the ambient pressure. The maximum meniscusseparation diameter (2R) for the baseline CTMFD apparatus used forstudies of the present disclosure was about 0.29 m, the sensitive volumebulb (about 2.3 cc) diameter is approximately 15 mm, and the wallthickness is close to 2 mm. Using these values, the induced negativepressure at the inside wall of the sensitive bulb can be calculated. Forsmall centerline P_(neg), (e.g. about −1 bar), there is an approximately15% difference between the P_(neg) at the centerline of the sensitiveregion and in the fluid at the wall of the sensitive region. However, asthe centerline P_(neg) increases to about −10 bar the difference reducesto about 8%. As is obvious, such reductions depend on the choice ofsensitive volume bulb's radius, r, relative to the meniscus radius R.

While, identifying TMFD fluids with only a single constituent atom forconducting experiments at room temperature is impractical, hydrocarbonsoffer a practical alternative, in that, at least for TMFD based neutronspectroscopy, they could be selected to “effectively” possess propertiesvery similar to an ideal monoatomic fluid. This is related to LET(dE/dx) for recoiling atoms. From Table 2 we see that the LET for H atomrecoils is relatively small (183 MeV/cm) despite the fact that neutronswill deposit more energy in collisions with H than with any other atom.Carbon (C), on the other hand, with 6 units of charge delivers asignificantly higher LET (about 4200 MeV/cm). As a result, for virtuallyall TMFD fluid choices, in relevant fast neutron detection conditions Hrecoils may be ignored (i.e., up until the nucleation P_(neg) thresholdbecomes small enough wherein, even proton recoils offer the CDEenablement). Additionally, as Table 2 data indicate, backgroundgamma-electron LET contributions would be ×100 lower and also safelyignored.

Notably, a 14 MeV neutron strike can create C ion recoils with up toabout 4 MeV from frontal interaction; and H recoils will be generated upto about 14 MeV under such conditions. With a 2.5 MeV neutron (e.g.,D-D) source, C ion recoils will be created up to 0.7 MeV and H recoilswill be created up to about 2.5 MeV. Referring to FIG. 2, relativeenergy deposition by Carbon and Hydrogen in 1825 Angstrom criticalbubble diameter (corresponding to −4.4 bar P_(neg)) in Heptane (C₇H₁₆)as modeled in SRIM is shown. From FIG. 2 it is seen that within acritical bubble diameter at −4.4 bar of negative pressure in Heptane (anadvantageous choice), a Carbon ion on the order of about 1 MeV iondeposits greater than 4 times as much energy into the critical diameter(<about 200 nm), than H recoils at any energy up to and includinghundreds of MeV. Thus, despite the greater energy initially imparted tothe Hydrogen atoms, the energy deposition for creating a critical sizedcavity is dominantly higher for Carbon atoms.

It is also important to note that the technique for determining thethreshold by ordering recoil deposition breaks down when the initialrecoil energy near the threshold exceeds the energy corresponding to theBragg peak. Ions born with higher energy than this amount of energy willhave a LET less than the LET at the Bragg Peak at the beginning of thetrack. However, as they slow down in the fluid, there will be a criticaldiameter over which they each have the opportunity to deposit anidentical amount of energy corresponding to the LET at the Bragg Peak(assuming they do not leave the detector). Thus, the fluid would beexpected to go from detecting all neutron elastic scatters depositingmore than the Bragg peak energy (and the algorithm sets the Bragg peakenergy to be the threshold) to not detecting any neutrons at all (andthe algorithm is unable to determine a threshold) within a very smallwindow of negative pressure. Fortunately, for isotopic and (D,D) or(D,T) fusion sources carbon recoil energies remain far below the Braggpeak energy of about 10 MeV (for Carbon in Heptane) as noted in FIG. 2.

The calculation of CDE thresholds assumes that there is only a singleparticle interaction depositing a portion of its energy within thecritical bubble radius (in the 10-100 nm range). In extremely highradiation environments, there theoretically could be coincidentinteractions that can collectively overcome the energy barriers forCDEs, even when individual particles would not; for instance, for CDEsfrom high intensity nanosecond UV laser pulse (mJ/pulse) inducedcavitation. However, this should not pose an issue for neutron detectionfrom most [Special Nuclear Material (SNM) detection related] practicalneutron sources emitting about 10⁵ n/s. For an example situation, thetotal number of interactions each depositing 410 eV within 100 nm in theCTMFD volume in Heptane as predicted by MCNP calculation is about 40/swithin the whole 2.3 cm³ cavity. The size of the critical radius is onthe order of 10⁻⁷ m at most. Thermal spike theory places a lower boundfor the bubblewall velocity is around 3 m/s and thus the time ofexpansion or heat dissipation is 10⁻⁷/3=3.3*10⁻⁸ s (although thetimescale for the energy to fully leave the bulb is significantlylonger). The size of the critical cavity is 4/3*π*(10⁻⁷ m)³=4.2*10⁻¹⁵cm³. Thus, the frequency of two neutrons depositing energy in the samecritical diameter space in coincidence before the heat dissipates isnegligible. Despite photons being emitted by both the ²⁵²Cf and thePu—Be source in the experiments performed (as well as the IR sensorsused to record CDEs), photons are not included in considerations fornucleation; this is because the linear energy transfer is negligiblecompared to that from neutron interactions. A CTMFD operating in theneutron CDE P_(neg) state regime convincingly cannot produce an eventdue to single photon interaction as long as the photon energy is notabove the photoneutron nuclear reaction threshold.

Many hydrocarbons have the desired property that LET from H recoils isnegligible compared to that from C recoils. In order to find an optimalfluid, candidates needed to be assessed on predicted Pu—Be fast neutronsource P_(neg) threshold (P*_(neg) ^(Pu—Be)), and vapor pressure. Table3 presents pertinent property variables for a range of possible choicesof TMFD fluids for SAS.

TABLE 3 Properties for hydrocarbons that were considered for SASapplication. Pvap Predicted P_(neg) Fluid (mmHg) (bar) Carbon density(g/cc) Isopentane (C₅H₁₂) 595 0 0.51 Hexane (C₆H₁₄) 130 −4.2 0.55Heptane (C₇H₁₆) 40 −4.4 0.57 Octane (C₈H₁₈) 11 −5.4 0.59 Nonane (C₉H₂₀)3.2 −6.8 0.61 Dodecane (C₁₂H₂₆) 1.5 −8.7 0.64

The P*_(neg) ^(Pu—Be) nucleation threshold for a TMFD liquid is definedas the negative pressure (P_(neg)) that corresponds to an average timebetween CDEs of 100 s when a CTMFD similar to the one shown in FIG. 1was exposed to a Pu—Be neutron source emitting about 2*10⁶ n/s at adistance of 20 cm. A database of 25 experiments with 17 different TMFDfluids was prepared to correlate various fluid properties such assurface tension (s), heat of vaporization (H_(vap)), viscosity (m), etc.with the experimental P_(neg) thresholds. It was found that the P_(neg)correlated well with Hvap—something quite unexpected given thatpredictions using the well-known thermal spike theory (TST) declaresthis specific work term enabling CDE to be a very small component asseen in Table 1. Referring to FIG. 3, a TMFD detection fluid enthalpy ofvaporization vs. tension pressure (|P_(neg)|) thresholds for detectingfast neutrons from a Pu—Be isotope neutron source (1Ci Pu—Be sourcepositioned about 20 cm from a about 3 cc CTMFD, average detection timeof 100 s at a given P_(neg) is shown. The quadratic fit for the data setin FIG. 3 is shown in Eq. (4). The correlation coefficient (R²) is about0.8.

H _(vap)=0.1605*P _(neg) ²+0.6305*P _(neg)+26.036 (R ²=0.79)  (4)

Using this formulation, it was possible to predict, a priori, therequired P_(neg) for various fluids with reasonable accuracy. Acetone at22° C. was predicted to have a threshold of −4.64 bar and theexperimental value was −4.8 bar. Isopentane at −25° C. was predicted tohave a threshold of “1.86 bar and the experimental value is found by usto be between −2 and −2.5 bar. The formulation was then used to predictthe threshold that would be obtained with other hydrocarbons. Given thetesting apparatus and the near uniformity of fluid densities, it wasconsidered optimal to find a fluid with a threshold between −4 and −5bar. For fluids with thresholds below this P_(neg), the CTMFD went fromwholly insensitive to instantaneous detection with very small rotationalspeeds and hence, not feasible for use for SAS. It is pointed out thatthe correlation has limitations; it somewhat under-predicts the P_(neg)for fluids with very high and very low H_(vap) values such as forIsopentane (predicted=0 bar, measured=−1.1 bar) and Dodecane(predicted=−8.7 bar, measured=−11 bar); however, it offered acceptableaccuracy for the majority of typical TMFD fluids such as Heptane(predicted=−4.4 bar, measured=−4.4 bar).

When generating the data for FIG. 3, some of the fluids were identifiedas being very difficult to work with because of their high vaporpressure. Isopentane, for instance, with a vapor pressure of 595 mmHgwas difficult to keep at a constant 2R meniscus separation in the CTMFDdue to evaporation losses at room temperature, unless a specific sealingcap material is utilized (e.g., viton); otherwise, isopentane tends tochemically attack most materials like ordinary rubber. Acetone with avapor pressure of 180 mmHg at room temperature has proven to be areliable standard TMFD detection fluid in the past for fast neutronswithout significant evaporation loss. Thus, it was advisable to select afluid for SAS which not only offered a P_(neg) threshold in the −4 barrange, but also one which possessed vapor pressure at or below 180 mmHgat room temperature and one that did not attack most sealing caps. Whilenot immediately helpful in determining the nucleation threshold of thefluid, a higher density of C atoms for SAS is desirable due to theenhanced probability of scattering induced CDEs for a given neutronflux. Based on the information from Table 3, Heptane was selected forits low vapor pressure, P_(neg) threshold, and sufficiently high densityof Carbon atoms. Referring to FIG. 4, a CTMFD system geometry as modeledfor MCNPX-POLIMI code calculations is provided. MCNPX-POLIMI, a MonteCarlo neutron simulation tool was used to render and model in 3-D theinteraction of neutrons with the testing apparatus configuration (shownin FIG. 4). For each of 10⁹ (billion) neutrons (simulating a Pu—Beisotope neutron source spectrum), the resulting scatter interactions offof the C and H atoms in the bulb were recorded along with the specificXYZ position and the time of flight up to that collision. Referring toFIG. 5, a spectrum showing frequency of induced recoils in Heptane (inthe CTMFD sensitive volume) vs recoil energy of C atoms when subject toneutrons emitted from a Pu—Be isotope neutron source positioned about 35cm from the CTMFD bulb is shown. The collisions with C atoms andresulting interaction energetics information database were then used tocreate the recoil spectrum is shown in FIG. 5 which provides the numberof carbon recoils generated at or above the energy on the x-axis per 10⁹incident neutrons from a Pu—Be isotope neutron source positioned 35 cmaway as depicted in FIG. 4. The count rate frequency begins to stabilizetoward the eV range because the lower energy Pu—Be neutrons tend to leakaway (i.e., escape the detector volume) before they thermalize in theabsence of significant moderation in this particular systemconfiguration.

Control experiments were performed to establish that the TMFD was readyfor detection with negligibly low false positives. In none out of theten, one minute trials at a P_(neg) of −8 bar resulted in CDEs in theabsence of the Pu—Be or Cf-252 neutron source. The Pu—Be source(emitting about 2.4*10⁶ n/s) was then brought in and placed at adistance about 35 cm from the CTMFD for gathering data at variousP_(neg) states. For these runs, the time between CDEs (“wait time”) isdefined as the time it takes for a CDE to occur after the CTMFD isramped up in speed, and the targeted P_(neg) state is achieved (aprocess requiring about 5 s from a cold start). Data were acquired forP_(neg) states between −4.4 bar and −6.0 bar in 0.2 bar increments.Results are summarized in Table 4—the Error column includes both Poissonerror from the radiative process as well as systematic error induced bythe LABVIEW equipment for 3 s cycle time.

$\begin{matrix}{{{Poisson}\mspace{14mu} {Error}} = \frac{{Total}\mspace{14mu} {Wait}\mspace{14mu} {Time}}{\sqrt{{Number}\mspace{14mu} {of}\mspace{14mu} {Cavitiations}^{3}}}} & (5) \\{{Error} = \sqrt{{{Poisson}\mspace{14mu} {Error}^{2}} + {{System}\mspace{14mu} {Error}^{2}}}} & (6)\end{matrix}$

TABLE 4 Baseline experiment results for Heptane with the Pu—Be neutronsource at 35 cm. Negative pressure Average time CDEs within Wait time(bar) (s) between CDEs 60 s error (s) −4.4 97.24 14/30 25.99 −4.6 42.7121/30 9.33 −4.8 17.42 29/30 3.25 −5 5.00 30/30 0.96 −5.2 3.35 30/30 0.68−5.4 2.42 30/30 0.53 −5.6 1.52 30/30 0.41 −5.8 1.21 28/28 0.38 −6 1.0410/10 0.44

By comparing the CDE rate per source neutron emission obtainedexperimentally to the cumulative recoil generation rate below a givenenergy per neutron emission given by the MCNP simulation, it waspossible to determine the particular energy whereby the two generationrates are equal. This energy is thus determined to be the CDE detectionrecoil energy threshold (Eth). Depositions of energy onto a carbon atomexceeding Eth will be expected to cause a CDE, and consequently,depositions of energy onto a C atom of less than this amount will notcause a CDE.

Referring to FIG. 6, MCNP predicted recoil spectrum in comparison withexperimental neutron detection rates at various |P_(neg)| statescorresponding to recoil energy for nucleation is provided. FIG. 6graphically illustrates the process of Eth determination. The ‘RecoilSpectrum’ line depicts the MCNP calculated C recoil spectrum generatedin the sensitive bulb region of the CTMFD per 10⁹ particles emitted froma Pu—Be source placed in a location corresponding to the geometry of theexperiment shown in FIG. 4. The |P_(neg)|=‘6.0 bar’ line has a heightcorresponding to the number of particles detected experimentally in thetest at −6 bar per 10⁹ particles emitted from the source (i.e., 1 CDEevery 1.04 s as provided in Table 4). At the energy that the eventfrequency is the same for the ‘6.0 bar’ and ‘Recoil Spectrum’ lines, the‘6.0 bar’ line is drawn straight downward and the energy correspondingto the detection threshold for C recoils with a Pu—Be source at 6 bar isencountered. The ‘5.8 bar’ line represents the same process done inorder to determine the threshold at |P_(neg)|=5.8 bar.

Referring to FIG. 7, a graph of carbon recoil threshold in MeV vs.|P_(neg)| in bars is provided showing variations of carbon recoilinduced energy threshold for a CDE to occur vs the correspondingcenterline |P_(neg)|. If the process is repeated for each of theexperimental pressures, the full relationship between the negativepressure and the threshold energy can be obtained as is displayed inFIG. 7.

For each of 24 arithmetically distributed incident neutron energiesbetween 0.4 MeV and 10.4 MeV an MCNP simulation model was constructedwith a source centered at that given energy but slightly distributed tominimize the effect of neutron scattering cross-section resonance andplaced in the location of the PuBe source in the experiments. For everystrike on a Carbon atom in the simulation, the energy imparted wascompared to the response curve generated as discussed above. The radialposition of the strike was used to determine the localized(off-centerline if need be) P_(neg) in the CTMFD. Referring to FIG. 8, arelative count graph of neutron energy in MeV is provided in which aresponse matrix of the CTMFD system (FIG. 4)—relating detection ratesfor neutrons of various energies with |P_(neg)| states varying from 4.4bar to 6.0 bar. Thereafter, by repeating the above-mentioned process foreach neutron energy and each of the centerline negative pressure statesof the system, the full response matrix for the detector was derived asshown in FIG. 8. Depicted therein is the probability for a detectionevent to take place if a neutron is emitted at the experimental locationwith the energy on the x-axis and the CTMFD bulb with centerlinenegative pressure corresponding to the symbol in the legend. Because themaximum negative pressure of −6 bar was limited by the measurable waittimes in the chosen detector-source geometry, the minimum encounteredrecoil threshold for this set of experiments was 1.0062 MeV as seen inFIG. 7. As a result, there was no possibility for detecting at neutronenergies about 3.5 MeV. This is because neutrons are able to deposit viaelastic scattering at most 28.4% of their energy onto C atoms.

Referring to FIG. 9, a graph of relative response vs. neutron energy (inMeV) is provided showing PuBe neutron source spectrum and unfoldedapproximation using volume averaged model of CTMFD detection volume.Using the response of the CTMFD to the Pu—Be spectrum from theexperiment described above, it was possible to use the volume averagedresponse matrix discussed above and the unfolding code, BON, toreconstruct the spectrum of the original source as shown in FIG. 9. Asexplained earlier, because of the equipment constraints on wait time andthe experimental geometry, neutron energy bins at and below about 3.5MeV weren't possible to consider—by optimizing the source-detectorgeometry and increasing the source-to-detector distance it should befeasible to probe for lower energies but this was not done for the workreported herein. It is noted that the Pu—Be neutron spectrum over thevalid energy domain of the response matrix of FIG. 8 is reasonably wellcaptured from about 5 MeV to above 10 MeV. Instead of assuming that theentire CTMFD central volume is at the same negative pressure as at thecenterline, it is also possible to think of the central bulb (holdingthe sensitized fluid for CDEs) as being composed as concentric cylinderswith radii chosen such that the pressure gradient over the cylinderallows for a constant decrease in negative pressure from the inside edgeto the outside edge. Then, the sensitivity of the cylinders with thesame inside edge pressure but different experimental parameters can besolved for simultaneously. FIG. 10 depicts the sensitivity regions inthe detector bulb volume as the CTMFD rotates more rapidly and engendersa progressively more tensioned pressure state at the centerline. In FIG.10, all regions of the same color would now possess the same sensitivityfor neutron detection. The sensitivity of the outer colored cylindricalzones of the first diagram is nil; with increasing rotational speed, thesensitized zone branches outwards with the inner ones being moresensitive and so on. After generating carbon recoil curves for each ofthe concentric cylinders in the bulb volume for each of the centerlinenegative pressures, all of the cylinders with the same inside linenegative pressure were solved simultaneously by minimizing thedifference between the number of events above the various thresholds forcylinders in the same experiment and the experimental wait time of thatexperiment. Two methods were: a modified Newton's method, and, anInteger program implemented through OPENSOLVER. In the modified Newton'smethod, we define x to express the energy thresholds for each of thegroups of cylinders with the same sensitivity. F(x) expresses thedifference between the number of simulated events above the variousthresholds in the sensitivity cylinders summed across each simulatedexperiment and the experimentally determined number of events. J(x)expresses the change in the expected counts for each experiment inducedby a unit change in the threshold for each of the groups of cylinderswith the same sensitivity. As with any version of Newton's method.

v ^((n)) =−[J(x ^((n))]⁻¹ F(x ^((n)))  (7)

and

x ^((n+1)) =x ^((n)) +v ^((n))  (8)

Because of the shape of the function it became necessary to constrainthe step size. This was achieved by either constraining the length ofthe vector, v, or by constraining the magnitude of the elements of thevector. In this manner, solutions starting with x⁽⁰⁾=1 MeV for allcylinder groups matured into acceptable threshold solutions. In usingthe Integer program method, first, all of the recoil curves were fittedto by a set of linear splines. The linear program was then programmed tochoose thresholds such that the sum of the values on the splinedapproximation of the sensitivity cylinder recoil curves most closelymatched the experimentally encountered count rate. As is known, theInteger program method is guaranteed to converge to a “globally” optimalsolution, whereas the Newton's method solution is not guaranteed tooffer such promise (the tradeoff being that the splines areapproximations of the true recoil functions for the cylinders which areused directly by Newton's Method). Additionally, it is much easier toconstrain the solution space to realizable solutions using an Integerprogram than it is with Newton's method.

In relation to the recoil curve shown in FIG. 7, all the experimentswere required to use the same source in the same location in order toavoid the difficulties of having to combine experiments with the samethreshold but with widely different count rates. However, this resultedin a constraint for using data with CDE wait times that were very long,and consequently having large Poisson errors, and also CDE wait timesthat were very short—thus, introducing large errors due to uncertaintyin the CDE detection and event timing space. In order to be able tocombine disparate experiments, the count rate and the simulated recoilcurves were first scaled by the inverse of the Poisson error in theexperiment. In addition to using different locations, a ²⁵²Cf sourcewith intensity of about 7.9*10⁴ was used in some of the experiments.Another refinement included using a CTMFD with a larger, 40 cc,sensitive volume for some of the experiments to enable the use of morecylinders each with various specific detection thresholdssimultaneously. The experiment type combinations with assigned specificnumbers, are tabulated in Table 5 and the resulting experimental dataset and results are summarized in Table 6.

An experiment was selected to become the ‘unknown’ data set so that thespectrum of the Cf source neutrons used to create it could be solvedfor. Using the other 8 experiments, a recoil threshold curve wasconstructed just as in FIG. 7. Referring to FIG. 11, a graph of carbonrecoil energy vs. |P_(neg)| in bar is provided showing variations of Crecoil threshold energy with |P_(neg)| for volume averaged and LPinteger program models. Three solutions appear in FIG. 11. The ‘VolumeAveraged’ solution corresponds to the thresholds obtained by using thevolume averaged approach discussed above. The ‘Integer Program’ solutionis the curve obtained by the integer program solution using the radialmethod discussed above. The ‘Power Fit’ solution represents a power lawfit of the integer program solution. Power Fit was selected based onstriving for resemblance to the form expected by the well-known ThermalSpike Theory used for bubble chambers (but, as explained earlier failedfor TMFDs). The equation for the ‘Power Fit’ was derived as:

Carbon Recoil Energy=189.71*P _(neg) ^(−2.9)  (9)

Just as was done in the construction of FIG. 8, a series ofmonoenergetic neutrons were simulated originating from the unknownsource location (in this case corresponding to the geometry of theexperiment discussed above from Table 3). Events simulated inMCNPX-POLIMI to create carbon recoils with more energy than thethreshold established by the power fit solution of FIG. 11 were deemedto create a CDE. Referring to FIG. 12, relative counts of neutron energyin MeV is provided showing resulting response matrix corresponding tothe power law lift of FIG. 11. Simulations with each centerline negativepressure at each of the mono-energetic energies formed the responsematrix shown in FIG. 12. Finally, by using the experimental data fromExperiment 2 and the response matrix of FIG. 12 it was possible to usethe BON unfolding code to produce the unfolded spectrum as shown in FIG.13, wherein relative responses of neutron energy in MeV is presentedwhere Cf-252 neutron source spectrum and the corresponding unfoldedapproximation (using experimental data from Table 6 together with theresponse matrix of FIG. 12) are provided. This was also performed forthe volume averaged method described earlier using the same experimentsto form a similar response matrix and unfolded spectrum. As expected,the unfolding performed using the radial method discussed abovesignificantly outperformed the volume averaged method described above.The large radial component of the experiments with the 40 cc bulbsresulted in the importance of strike location being non-negligible. As aresult, the volume averaged solution predicted thresholds that werehigher than the true thresholds. Thus, it would appear that the radialmethod will be required for real world spectroscopy application withlarge volume CTMFDs.

Experiments were separately conducted with known monoenergetic neutronsin order to independently validate the predictive capability of theas-derived carbon recoil based response curves derived from isotopicneutron sources. This included experiments using a D-T generatorproducing 14.1 MeV neutrons at an intensity of about 1.3*10⁷ n/s, andexperiments using a D-D neutron generator producing 2.45 MeV neutrons atan intensity of about 2.6*10⁷ n/s. The P_(neg) tension pressure statescorresponding to the maximum wait time for a CDE distinctlydistinguishable from background was determined to be “4.1 bar (for 14MeV neutrons), and “7.3 bar (for 2.45 MeV neutrons), respectively. AMCNPX-POLIMI simulation was constructed to obtain the recoil spectrumsuch that it could be matched to the experimental count rate as was doneearlier. Assuming the entire bulb had equal sensitivity to the highenergy neutrons, the calculated corresponding C recoil energy thresholdswere about 4.0 MeV and 0.7 MeV, respectively for incident 14 MeV and2.45 MeV neutrons (given that 4.0=about 14.1*0.284 and 0.7=about2.45*0.284). The multiplier 0.284 is derived from elastic scattering ofneutron with a C atom [i.e., 0.284=1−(A−1)²/(A+1)², where A=12 for C].Assuming instead that all counts originated within 0.1 cm of thecenterline, using the simulation, the implied threshold for the 14 MeVneutron scatters reduced to about 3.42 MeV while the threshold for 2.45MeV neutrons remained virtually the same at about 0.70 MeV. Using thePower Fit described herein, the thresholds expected at −4.1 and −7.3 barrespectively were 3.171 and 595 MeV (quite close to the experimentalvalues of =3.2 and 0.7 MeV), providing added evidence for applicabilityof SAS over the 2.45 MeV to 14 MeV neutron energy range.

Referring to FIG. 14 a graph of carbon recoil energy (eV) vs. carbonrecoil range (A) is presented where calculated carbon recoil range curvein heptane is provided. Using SRIM, the relationship between the energyof an energetic C ion and the LET as that ion traverses the Heptane wasderived. This information is presented in FIG. 14. Using thisrelationship, it was possible to transition from describing the amountof energy required to be delivered to the C atoms in order to causeCDEs, to now assessing for the amount of energy that needs to bedeposited within a critical radius (in the TMFD fluid—heptane), in orderto cause CDEs. Thus, enabling the results from the recoil thresholdcurves to be compared to predictions for CDE onset predicted by theclassical TST we have discussed earlier. The experimentally obtainedthresholds from mono-energetic (2.45 MeV and 14 MeV) neutrons areincluded in FIG. 15 and, de facto act as anchors at the lower and upperbounds in the P_(neg) range. Referring to FIG. 15, predicted energybarrier in heptane (measured in eV) vs. |P_(neg)| in bar is presented,where predicted required energy thresholds for CDEs from neutron inducedC recoils vs |P_(neg)| for various techniques compared with predictionsfrom Thermal Spike Theory are provided—included are estimates fromexperiments with DD(2.45 MeV) and DT (14 MeV) accelerator neutronsources. From the results plotted in FIG. 15, it is obvious that thepredicted results from our recoil curves enable a reasonably accuratecapability for fast neutron spectroscopy over the 2.5 MeV to 14 MeVrange; in sharp contrast to the vast under-predictions from the ThermalSpike Theory (TST) widely used for predicting energy thresholds inclassical bubble chambers and superheated droplet detectors.

The following protocol can be used for obtaining spectroscopy in otherfluids besides heptane.

1. Acquire CDE data with several source-detector geometries across allwait times where the count rate is distinguishable from background andsmall enough to be measured, 2. Model those geometries in MCNPX-POLIMIand determine the recoil spectrum, 3. Use volume averaged and/or radialmethods to establish the recoil curve, 4. Simulate mono-energeticsources in the source-detector geometry to be used in the problem anduse the recoil curve to determine then number of nucleation events toform the response matrix, 5. Take data with the unknown source, 6. Feedthe response matrix and the experimental data from the unknown sourceinto the BON unfolding code, and finally utilize the as-coded SAScomputer code “Output”, and 7. Computer program Output displays resultsof the unfolded spectrum of the unknown neutron source.

For fluids where the recoil curve has already been established steps 1-3can be skipped. For fluids with known response curves and geometrieswith already developed response matrices, steps 1-4 can be skipped.Because steps 1-4 are all performed ahead of time and steps 6-7 can beperformed in less than 1 s, the amount of time required to getspectroscopic information depends on the time it takes for dataacquisition. The ‘experiment 2’ data set used for unfolding in thispaper included 428 CDEs with an average time to detection of 27.8 sacross 16 negative pressures for a total of 3.3 h of sensitive time.Using larger numbers of detectors and fewer negative pressures it shouldbe possible to substantially reduce the time to spectrum to meet currentDepartment of Homeland Security needs of less than 20 s perinterrogation.

Referring to FIG. 16, a schematic diagram for a system comprising one ormore detectors for solving [EV]=[RM]×[NE], where EV is a vector matrixof results of relative detection time for a range of P_(neg) statesobtained experimentally by the placement of one or more detectorsequidistance from an unknown neutron source, NE is a neutron energyvector, RM is a response matrix, and P_(neg) is the tensioned negativepressure.

Referring to FIG. 17, a flowchart outlining operations embodied in thepresent disclosure are provided spanning three pages for deriving theresponse matrix.

The following references are related to the present disclosure, entiretyof each of which is incorporated herein by reference into the presentdisclosure.

Those skilled in the art will recognize that numerous modifications canbe made to the specific implementations described above. Theimplementations should not be limited to the particular limitationsdescribed. Other implementations may be possible.

REFERENCES

-   [1] Rusi Taleyarkhan, J. Lapinskas, Y. Xu, Tensioned metastable    fluids and nanoscale interactions with external    stimuli—Theoretical-cum-experimental assessments and nuclear    engineering applications, Nucl. Eng. Des. 238 (7) (2008) 1820-1827.-   [2] T. F. Grimes, J. A. Webster, B. A. Archambault, R. P.    Taleyarkhan. Applications of Tension Metastable Fluid Detectors in    Active Neutron/Photon SNM Interrogation Systems, IEEE, HST    Conference Transactions, Paper 46, 978-1-4799-1737-2/15, 2015.-   [3] Frederick Seitz, On the theory of the bubble chamber, Phys.    Fluids (1958-1988) 1 (1) (1958) 2-13.-   [4] C. D. West, Cavitation Bubble Nucleation by Energetic Particles,    Oak Ridge National Laboratory, Oak Ridge, Tenn., 1998, No.    ORNL/TM-13683.-   [5] T. F. Grimes, J. A. Webster, B. A. Archambault, R. P.    Taleyarkhan. Applications of tension metastable fluid detectors in    active neutron/photon SNM interrogation systems, Poster Session IEEE    HST 2015 Conference, 2015.-   [6] Glenn F. Knoll, Radiation Detection and Measurement, John Wiley    & Sons, 2010.-   [7] L. Briggs, A new method for measuring the limiting negative    pressure in liquids, Science. 109 (1949) 440.-   [8] James F. Ziegler, Matthias D. Ziegler, Jochen P. Biersack,    SRIM—The stopping and range of ions in matter (2010), Nucl. Instrum.    Methods Phys. Res. Sect. B: Beam Interact. Mater. Atoms    268 (11) (2010) 1818-1823.-   [9] T. F. Grimes, et al. Gamma-blind transformational nuclear    particle sensors, IEEE HST Conference Transactions,    978-1-4673-2709-1/12, 417-422, 2012.-   [10] Sara A. Pozzi, Enrico Padovani, Marzio Marseguerra,    MCNP-PoliMi: a Monte-Carlo code for correlation measurements, Nucl.    Instruments Methods Phys. Res. Sect. A: Accel. Spectrom. Detect.    Assoc. Equip. 513 (3) (2003) 550-558.-   [11] R. S. Sanna, A Manual for BON: A Code for Unfolding Multisphere    Spectrometer Neutron Measurements, EML-394, August 1981.-   [12] Brian Bradie, A Friendly Introduction to Numerical Analysis,    Pearson Prentice Hall, Upper Saddle River, N.J., 2006.-   [13] A. J. Mason, OpenSolver—an open source add-in to solve linear    and integer progammes in excel, Operations Research Proceedings    2011, 2012. pp. 401-406.-   [14] T. F. Grimes, Nucleation and Detection in Tensioned Metastable    Fluids (Ph.D. dissertation), Purdue University, 2015.-   [15] ANSI, American National Standard Performance Criteria for    Spectroscopy-Based Portal Monitors Used for Homeland Security,    Technical Report ANSI 42.35, American Nuclear Standards Institute,    Washington, D.C., 2007.

1. A portable system for detecting neutrons comprising, a detectorliquid in a first enclosure having walls and a venturi valve system suchthat the detector liquid can pass therethrough during detectoroperation, the enclosure affixed to a spinning mechanism for introducingnegative pressure in the detector liquid, wherein the spinning mechanismis capable of inducing a negative pressure in the detector liquid suchthat neutron detection can occur in the detector liquid at negativepressure and configured to detect neutron-caused vapor pocketcorresponding to neutron counts, wherein the detection is based on[EV]=[RM]×[NE], where EV is a vector matrix of results of relativedetection time for a range of P_(neg) values obtained experimentally byplacing one or more detectors equidistance from an unknown neutronsource, NE is a neutron energy vector, RM is a response matrixrepresenting a probability matrix for detecting a neutron at a pluralityof P_(neg) values, and P_(neg) is the tensioned negative pressure.